(a)

\begin{aligned} & N =\operatorname{masin} \theta+ mg \cos \theta \\ & mg \sin \theta= ma \cos \theta \\ & a = g \tan \theta \\ & \therefore N = mg \frac{\sin ^2 \theta}{\cos \theta}+ mg \cos \theta \\ & N = mg \left\{\frac{\sin ^2 \theta+\cos ^2 \theta}{\cos \theta}\right\}=\frac{ mg }{\cos \theta} \\ & N =\frac{ mg }{\cos \theta} \end{aligned}